8.1 Introducing Statistics: What Is the Best Way to Compare Groups?

• Categorical variables can be counted or measured numerically.

  False
• Provide an example of a categorical variable.

  Colors of cars
• What is the purpose of a hypothesis in research?

  Predict study's results
• Categorical variables group observations into distinct categories
• What is the primary difference between a research question and a hypothesis?

  Purpose and structure
• What statistical methods are used for categorical variables?

  Chi-square tests and cross-tabulations
• Steps to perform a chi-square test:

  1️⃣ Formulate hypotheses

  2️⃣ Construct a contingency table

  3️⃣ Calculate expected frequencies

  4️⃣ Compute the chi-square statistic

  5️⃣ Determine degrees of freedom

  6️⃣ Compare the statistic to the critical value
• The null hypothesis in a chi-square test states that there is no relationship between the variables.

  True
• To determine the p-value in a chi-square test, the calculated test statistic is compared to a critical value based on the degrees of freedom.
• Numerical variables measure or count data with numerical values.

  True
• A research question guides the study's direction, while a hypothesis predicts its expected outcome.
• To compare groups with categorical variables, the appropriate statistical method is the chi-square test.
• Categorical variables classify observations into categories
• Numerical variables are used in chi-square tests.

  False
• A hypothesis is always stated as a declarative sentence.


  True
• What are the two types of categorical variables?

  Nominal and Ordinal
• A hypothesis is always testable with data.


  True
• For numerical variables, the appropriate statistical methods are t-tests and ANOVA
• The appropriate statistical method to compare groups when dealing with categorical variables is the chi-square test.
• A contingency table organizes data with rows representing one variable and columns representing the other to analyze their relationship.
• If the p-value is less than the significance level, you reject the null hypothesis.

  True
• Match the variable type with its characteristic:

  Categorical Variables ↔️ Classify observations into categories

  Numerical Variables ↔️ Measure or count quantities
• A hypothesis is stated as a declarative sentence and can be tested with data.


  True
• Steps to perform a chi-square test

  1️⃣ Formulate hypotheses

  2️⃣ Construct a contingency table

  3️⃣ Calculate the test statistic

  4️⃣ Determine the p-value

  5️⃣ Interpret the results
• What type of variables group observations into categories without a numerical value?

  Categorical variables
• Match the type of variable with its characteristic:

  Nominal ↔️ Groups without order

  Ordinal ↔️ Groups with order

  Discrete ↔️ Countable values

  Continuous ↔️ Infinite values
• The research question identifies the variables and their relationship
• Give an example of a research question.

  Does daily exercise affect weight loss?
• T-tests are used to analyze categorical variables.

  False
• Match the aspect with its description:

  Purpose of Research Question ↔️ Guide the study's direction

  Purpose of Hypothesis ↔️ Predict the study's results

  Structure of Research Question ↔️ Posed as a question

  Structure of Hypothesis ↔️ Stated as a sentence
• Identifying the type of variable is crucial for selecting the correct statistical approach.


  True
• Steps to perform a chi-square test

  1️⃣ Formulate hypotheses

  2️⃣ Construct a contingency table

  3️⃣ Calculate the test statistic

  4️⃣ Determine the p-value

  5️⃣ Interpret the results
• What is the formula for the chi-square test statistic?

  $\chi^{2} =$$\sum \frac{(Observed - Expected)^{2}}{Expected}$
• Categorical variables group observations into distinct categories without numerical meaning.
• Match the variable type with the appropriate statistical method:

  Categorical Variables ↔️ Chi-square tests

  Numerical Variables ↔️ t-tests
• If the p-value is less than the significance level, you reject the null hypothesis.